1) The above transformation is a rotation about the point (2, 1.5)
Describe how you can prove that the two are in fact congruent. Use complete sentences.
2)Given a triangle with vertices at points
(-4, -10), (-8, -8), (-1, -1)
and the transformed triangle via translation at
(4,-7), (0,-5), ( 7, ?)
What is the missing new y coordinate? * I think it is 3
I do not understand the first one.
For number 2 :
-1 + 3 = 2 not 3
1) To prove that the two transformations are congruent, we first need to determine the type and amount of transformation that was applied to the original shape. In this case, we are told that it is a rotation about the point (2, 1.5).
To demonstrate that the two shapes are congruent, we should perform the following steps:
1. Plot the original and transformed shape on a graph using the given coordinates.
2. Determine the center of rotation by identifying the point (2, 1.5) on the graph.
3. Measure the angle of rotation by connecting the corresponding vertices of the original and transformed shape to the center of rotation.
4. Compare the lengths of the sides and measure the angles of both the original and transformed shape to ensure they are equal.
5. If all corresponding sides and angles are equal, we can conclude that the two shapes are congruent.
2) We are given the vertices of a triangle: (-4, -10), (-8, -8), (-1, -1). We are then provided the transformed vertices after a translation: (4, -7), (0, -5), (7, ?).
To find the missing new y-coordinate, we can use the fact that a translation is a shift in the x and y coordinates of a shape. In this case, the x-coordinate of the missing vertex is 7, which means it has experienced a horizontal shift of +7 units.
To determine the corresponding y-coordinate, we need to consider the vertical shift that the other vertices have undergone. The original coordinates of the second vertex are (-8, -8), and after the translation, it becomes (0, -5). This means that it has shifted vertically by +3 units.
Applying the same vertical shift of +3 units to the original y-coordinate of the missing vertex, which is -1, we can calculate the missing new y-coordinate as follows:
-1 + 3 = 2.
Therefore, the missing new y-coordinate for the transformed triangle is 2.